A Chance Discovery

One evening, I was on the telephone and the conversation had got rather boring. Not being able to hang up, I started aimlessly keying numbers into my desktop calculator…

At some point, I typed in 47 and repeatedly pressed the square root key. After three times, my calculator showed me a result, which made me raise my brows:

1.6181255

I was very surprised to see the first four digits of the golden ratio making up the result. Since I pressed the square root key three times, I must have taken the 8th root of 47, so that one can write:

where is the usual symbol for the golden ratio.

Throughout history, the golden ratio has attracted the interest of artists and architects. The proportion has been used in many of their works and a lot has been written about this particular number.